How do you find the domain and range of #y=5/(x-3)#?

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Answer 1 · 2018-06-06T15:31:00

The domain is #x in (-oo,3)uu(3,+oo)#. The range is #y in (-oo,0)uu(0, oo)#.

The denominator must be #!=0#.

Therefore,

#x-3!=0#

#=>#, #x!=3#

The domain is #x in (-oo,3)uu(3,+oo)#

To calculate the range, proceed as follows :

Let #y=(5)/(x-3)#

#y(x-3)=5#

#yx-3y=5#

#xy=5+3y#

#x=(5+3y)/(y)#

The denominator must be #!=0#.

#y!=0#

The range is #y in (-oo,0)uu(0, oo)#

graph{5/(x-3) [-52, 52.03, -26, 26.03]}